With max fuel it's not going to have any additional weight to spare for cargo. Because the MGTOW (which is also the inflight weight limit) is set at 590 the KC-10 can't even fuel up to 356K. I don't think it ever could-I doubt the 10 ever weighed 234K basic weight, let alone operating. 240 is the lowest I've ever heard. And that was from the 80s. Today, the average op weight for a "B" config jet (16 seats, 23 PPs), no pods, is roughly 250K. Add 340K fuel and you're at the max weight: 590K. That was the answer to the first criteria: max range unrefueled no cargo. 10,000 NMs sounds about right.. That's about 145 in the main tanks, 54 in the forward, 76 in the center and 64 in the aft.

Max cargo/ max fuel in a "B" config with a 250 Op weight. 164K of cargo, 145 in the mains and about 31K in the center. You can't really put alot of fuel in the forward and aft tanks because of zone load limits, ie, the aircraft's floor limitations. You can put alot of fuel underneath the floor or alot of cargo on top of the floor, but when you're hauling both you can carry less of both. It's a give and take: more cargo, less fuel in the Forward and aft tanks. More fuel in the forward and aft tanks, less cargo you can carry. For that, 3800 NMs sounds about right.